Solve for $x$ and $y$ using elimination. ${2x-3y = -19}$ ${-3x+3y = 15}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {2x-3y = -19}\thinspace$ to find $y$ ${2}{(4)}{ - 3y = -19}$ $8-3y = -19$ $8{-8} - 3y = -19{-8}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 4}$ into $\thinspace {-3x+3y = 15}\thinspace$ and get the same answer for $y$ : ${-3}{(4)}{ + 3y = 15}$ ${y = 9}$